In the context of the transition flow between highly collisional plasma and collisionless sheath, the linearized Fokker-Planck equation for the ions, in an intermediate collisionality region, is generalized to include an arbitrary source function. Nonisentropic effects due to the source function impact the isotropic part of the distribution function. A Legendre polynomial decomposition is performed up to an arbitrary order, and the problem for the first Legendre component is treated. Analytic expansions around zero and infinite velocities are performed, and a general solution for the distribution function is found. The treatment of the weakly collisional region, up to second order in the ratio of the mean free path over the scale height of the system, is discussed. The governing equations for this problem are laid out, and the methods of solving them are presented in detail.